Climate change is hard to account for.

The first difference is that carbon dioxide is not like other pollutants… The typical climate-policy targets that get thrown around — reducing emission rates by 80 percent by 2050, for example — are relatively meaningless. They focus on the rate of flow from the faucet. But that’s not what matters. What matters is the amount in the tub. If the tub fills up enough, global average temperature will rise more than 2 degrees Celsius and we’ll be in trouble. Avoiding that — staying within our “carbon budget” — is the name of the game.

The climate change that takes place due to increases in carbon dioxide concentration is largely irreversible for 1,000 years after emissions stop. Following cessation of emissions, removal of atmospheric carbon dioxide decreases radiative forcing, but is largely compensated by slower loss of heat to the ocean, so that atmospheric temperatures do not drop significantly for at least 1,000 years.

Climate change is notoriously tricky to deal with in standard economic terms. Part of it is that, to any normal person, something which is irreversible for 1,000 years sounds at least ten times worse than something which is irreversible for 100 years, if not even worse still.

Economically, though, the two are essentially the same. "Present value" is an economic concept dealing with the fact that money in the future is worth less than money now – because you can always invest money now and have more money in the future. Of course, that assumes long-term growth, which, if we're talking about world-changing events like anthropogenic climate change, might not be a safe assumption.

But the end result of the calculations is that nearly any cost beyond a hundred years into the future isn't worth spending money today to avoid. The intuitive conclusion – that it's worth fighting climate change harder if it will last for a millennium than a century – isn't the case. Assuming growth.

But there are even bigger problems for climate change than that. The vast majority of economic responses to it require calculating a "likely cost", and then applying that to the measures proposed to combat it. So, for example, a properly implemented carbon tax requires a calculation of the damage one tonne of CO2 does to the environment, in order to accurately price in the negative externalities.

Unfortunately, conventional ways of pricing risk rather fall over when considering something like climate change, because it carries a non-zero risk of existential threat. That is, there are proposed mechanisms[5] whereby "runaway climate change" could present a civilisation-ending threat.

How do you price the end of civilisation? One option is to look at the value of everything in the world. It would be quite an accounting task, and one faced by the UK government last year when they had to put a price on Stonehenge[6] to fulfil new bookkeeping requirements. The American government puts the value of the entirety of the US at $110trn[7], so it seems likely that the value of all the world's civilisations is well into 16 figures.

That's high, but it's countable. The real issue comes when you look at an alternative way of measuring the cost of risk, which is the amount you would pay to prevent it. Presumably, there is no sum which would not be worth spending to prevent the end of civilisation. Any cost would be less than the destruction of everything.

By that measure, then, the damage caused by an existential threat is infinite. But the problem with infinite quantities is that they don't work very well in conventional mathematics. Back to the normal risk accounting: you typically multiply the damage you are risking with the chance it will happen. So we are happy to suffer high risk of low damage – like groping for a glass of water at midnight with the lights off – or low risk of high damage – like driving a car – but not high risk of high damage – like driving a car at midnight with the lights off.

But infinity multiplied by anything other than zero is still infinity. Conventional risk assessment simply falls apart when confronted with something the magnitude of the worst possibilities of climate change.

Note too that it doesn't require the risk to be large. I think the risks of climate change are greater than most, but I also think it's extraordinarily unlikely that it actually would result in the end of civilisation. But can we rule it out with certainty?

The best way to look at it is to compare it to our every day lives. Thousands of people are killed crossing the road every day. To do so carries a non-negligible personal existential threat – that is, you might die. Yet I see people dodging traffic to get to work 30 seconds earlier every day, which suggests that, instinctively, we don't treat the risk of death with as much weight as we perhaps should.

But I think theres a different motivator at work. We know death is bad, and that it's worth doing a lot to try and avoid it; but we also know death can come from any corner. And the same is true of fighting existential threats to civilisation. If we could spend ludicrous sums to eliminate them all, it might be worth it; but who's to say we won't prevent climate change, only to die from an asteroid hit? Or cap our future development by not experimenting with nanotech, only for an angry AI to kill us in our sleep?

Climate change could be very, very bad indeed. But making the important choices about the trade-offs we should make to fight it are hard because, not despite, its seriousness.